A man’s age is four times that of his son in 20 years he will be only twice as old as his son. Find his present age.

Let's define the variables:
- Let \( x \) be the son's current age.
- Let \( 4x \) be the man's current age (since the man's age is four times the son's age).

In 20 years:
- The son's age will be \( x + 20 \).
- The man's age will be \( 4x + 20 \).

According to the problem, in 20 years, the man's age will be twice the son's age. Thus, we can write the equation:

\[ 4x + 20 = 2(x + 20) \]

Now, solve the equation step-by-step:

1. Expand the right-hand side:
   \[ 4x + 20 = 2x + 40 \]

2. Subtract \( 2x \) from both sides to get all the \( x \)-terms on one side:
   \[ 4x - 2x + 20 = 40 \]
   \[ 2x + 20 = 40 \]

3. Subtract 20 from both sides to isolate the \( x \)-term:
   \[ 2x = 20 \]

4. Divide by 2:
   \[ x = 10 \]

So, the son's current age is 10 years old. The man's current age is:
\[ 4x = 4 \times 10 = 40 \]

Thus, the man's present age is 40 years old.

Would you like more details or have any questions about this problem?

Here are 5 related questions you might ask next:
1. How do you solve systems of linear equations?
2. Can you explain the concept of age problems in algebra?
3. What are the methods to check the solution of an equation?
4. How can we set up equations for different age-related problems?
5. What is the significance of defining variables in solving word problems?

**Tip:** When solving word problems, carefully define your variables and set up equations based on the relationships described in the problem.

Learn how to solve a mathematical problem involving age relationships between a man and his son. This problem uses algebraic concepts to determine the present age of the man based on future age predictions. Suitable for students in Grades 7-9.

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